[" (c) "vec r*(4hat i-12j-3k)-0],[" The DCs of the line "6x-2=3y+1=2z-2" are "]

(i) Find the vector equation of a line passing through a point with position vector 2hat(i)-hat(j)+hat(k) , and parallel to the line joining the points -hat(i)+4hat(j)+hat(k) and hat(i)+2hat(j)+2hat(k) . Also find the cartesian equivalent of this equation. (ii) The cartesian equations of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find vector equation of the line.

By computing the shortest distance determine whether the following pairs of lines intersect or not: vec r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d vec r=(2 hat i- hat j)+mu( hat i+ hat j- hat k) vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) . (x-1)/2=(y+1)/3=za n d(x+1)/5=(y-2)/1; z=2 (x-5)/4=(y-7)/(-5)=(z+3)/(-5)a n d(x-8)/7=(y-7)/1=(z-5)/3 .

By computing the shortest distance determine whether the following pairs of lines intersect or not: vec r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d vec r=(2 hat i- hat j)+mu( hat i+ hat j- hat k) vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) . (x-1)/2=(y+1)/3=za n d(x+1)/5=(y-2)/1; z=2 (x-5)/4=(y-7)/(-5)=(z+3)/(-5)a n d(x-8)/7=(y-7)/1=(z-5)/3 .

By computing the shortest distance determine whether the following pairs of lines intersect or not: vec r=( hat i- hat j)+lambda(2 hat i+ hat k)a n d vec r=(2 hat i- hat j)+mu( hat i+ hat j- hat k) vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) . (x-1)/2=(y+1)/3=za n d(x+1)/5=(y-2)/1; z=2 (x-5)/4=(y-7)/(-5)=(z+3)/(-5)a n d(x-8)/7=(y-7)/1=(z-5)/3 .

If line vec r=( hat i-2 hat j- hat k)+lambda(2 hat i+ hat j+2 hat k) is parallel to the plane vec r.(3 hat i-m hat k)=14 , then the value of m is (1). 2 (2) -2 (3) 0 (4) 3

Consider the following 3 lines in space L_1: vec r= 3hat i-hat j+ 2hat k + lambda(2hat i + 4hat j-hat k) , L_2 :vec r =hat i+hat j- 3hat k + mu(4hat i + 2hat j+ 4hat k) and L_3 : vec r = 3hat i+2hat j- 2hat k + t(2hat i+hat j+ 2hat k) Then which one of the following pair(s) are in the same plane.

If vec a=2hat i+2hat j-3hat k,vec b=hat i-2hat j+2hat k,vec c=4hat i+3hat j+3hat k then find the value of |vec a+2vec b+2vec c|

Given that vec u=hat i-2hat j+3hat k;vec v=2hat i+hat j+4hat k;vec w=hat i+3hat j+3hat k and (vec u*vec R-15)hat i+(vec v*vec R-30)hat j+(vec w*vec R-20)hat k=0 Then find the greatest integer less than or equal to |vec R|

If vec x=3hati - 6hatj - hatk , vec y=hat i+4hat j-3hat k and vec z=3hat i-4hat j-12hat k then the magnitude of the scalar projection of vec x timesvec y on vec z is:

Find the equation of the plane through the line of intersection of : vec(r). (2 hat(i) - 3hat(j) + 4 hat(k) ) = 1 and vec(r). (hat(i) - hat(j) ) + 4 = 0 and perpendicular to the plane vec(r). (2 hat(i) - hat(j) + hat(k)) + 8 = 0 . hence, find whether the plane thus obtained contains the line: x - 1 = 2y - 4 = 3z - 12.